Earlier quoted context omitted.
Personally I use this tool I built as a Photoshop action over a decade ago, https://www.hcs.harvard.edu/~jrus/colortheory/jl.html (see the animation at the bottom showing almost precisely what you are asking about) Initial discussion: https://www.ledet.com/margulis/2010HTM/ACT08-Jacobs_Ladder.h... An HSV hue shift (or whatever similar thing you are thinking of) yields horrible results in this use case.
That example looks like it's working directly with RGB, which I expect to be correct. I've also seen it work well in HLS. But I worked on a tool where we were told to change from HLS to CIELab because it would be better, and it turned out to be much worse in practice.
Photoshop is definitely designed RGB-first, and some of the tools get a bit clunky in CIELAB mode. It is still an improvement for most of what I want to do.
I have many ideas for better image color manipulation tools.